1. Ordinary differential equations of first order. Basic concepts. Maximal solution. Existence and uniqueness of maximal solution
of the initial value problem., 2. Separable differential equations. Homogeneous differential equations of first order. Exact
equation. Linear differential equation of first order. Bernoulli equation., 3. Systems of differential equations in normal
form. Fundamental set of solutions of homogeneous linear systems. The Wronskian., 4. Linear differential equations of 2-nd
order. Method of undetermined coefficients., 5. Autonomous systems. Dynamic interpretation in the phase space., 6. Homogeneous
linear autonomous systems. The Euler method for the general solution., 7. Phase diagram of the homogeneous linear autonomous
system in the plane. Various types of equilibrium points. Nonhomogeneous linear autonomous systems., 8. Nonlinear autonomous
systems. Properties of phase trajectories. First integral., 9. Infinite series of numbers. Tests of convergence for the series
with positive terms., 10. Series with arbitrary real terms. Absolute and conditional convergence. The Leibnitz test., 11.
Power series. Structure of the domain of convergence and determination of the domain., 12. Operations on power series (multiplication,
differentiation, and integration of power series)., 13. The expansion of a function into the Taylor/MacLaurin series., 14.
Application of power series to the solution of the initial value problem for the linear differential equation of 2-nd order
with variable coefficients.